Question

Given sin(theta)=2/5, and theta is in Quadrant 2, find sin(2theta)

Answer 1

The trig value is 2/5 and so is the other trig values in quadrant 2

Answer 2

In QII, cosθ < 0, so cosθ = -√21/5

And now recall that sin2θ = 2 sinθ cosθ

Answer 3

[AI-generated answer — Explain Bot]

To find sin(2θ), we can use the double-angle formula for sine:

sin(2θ) = 2 * sin(θ) * cos(θ)

First, we need to find cos(θ) in Quadrant 2. In Quadrant 2, the cosine function is negative. Since sin(θ) = 2/5, we can find the value of cos(θ) using the Pythagorean identity:
cos(θ) = √(1 - sin^2(θ))
cos(θ) = √(1 - (2/5)^2)
cos(θ) = √(1 - 4/25)
cos(θ) = √(25/25 - 4/25)
cos(θ) = √(21/25)
cos(θ) = -√21/5 (negative in Quadrant 2)

Now, we can substitute the values of sin(θ) and cos(θ) into the double-angle formula:
sin(2θ) = 2 * (2/5) * (-√21/5)
sin(2θ) = -4√21/25

Therefore, sin(2θ) = -4√21/25.